hyperplonk/poly-iop/src/sum_check/mod.rs

//! This module implements the sum check protocol.
//! Currently this is a simple wrapper of the sumcheck protocol
//! from Arkworks.

use crate::{
    errors::PolyIOPErrors,
    structs::{DomainInfo, IOPProof, IOPProverState, IOPVerifierState, SubClaim},
    transcript::IOPTranscript,
    virtual_poly::VirtualPolynomial,
    PolyIOP,
};
use ark_ff::PrimeField;
use ark_std::{end_timer, start_timer};

mod prover;
mod verifier;

/// Trait for doing sum check protocols.
pub trait SumCheck<F: PrimeField> {
    type Proof;
    type PolyList;
    type DomainInfo;
    type SubClaim;
    type Transcript;

    /// extract sum from the proof
    fn extract_sum(proof: &Self::Proof) -> F;

    /// Initialize the system with a transcript
    ///
    /// This function is optional -- in the case where a SumCheck is
    /// an building block for a more complex protocol, the transcript
    /// may be initialized by this complex protocol, and passed to the
    /// SumCheck prover/verifier.
    fn init_transcript() -> Self::Transcript;

    /// Generate proof of the sum of polynomial over {0,1}^`num_vars`
    ///
    /// The polynomial is represented in the form of a VirtualPolynomial.
    fn prove(
        poly: &Self::PolyList,
        transcript: &mut Self::Transcript,
    ) -> Result<Self::Proof, PolyIOPErrors>;

    /// Verify the claimed sum using the proof
    fn verify(
        sum: F,
        proof: &Self::Proof,
        domain_info: &Self::DomainInfo,
        transcript: &mut Self::Transcript,
    ) -> Result<Self::SubClaim, PolyIOPErrors>;
}

/// Trait for sum check protocol prover side APIs.
pub trait SumCheckProver<F: PrimeField>
where
    Self: Sized,
{
    type PolyList;
    type ProverMessage;

    /// Initialize the prover to argue for the sum of polynomial over
    /// {0,1}^`num_vars`
    ///
    /// The polynomial is represented in the form of a VirtualPolynomial.
    fn prover_init(polynomial: &Self::PolyList) -> Result<Self, PolyIOPErrors>;

    /// receive message from verifier, generate prover message, and proceed to
    /// next round
    ///
    /// Main algorithm used is from section 3.2 of [XZZPS19](https://eprint.iacr.org/2019/317.pdf#subsection.3.2).
    fn prove_round_and_update_state(
        &mut self,
        challenge: &Option<F>,
    ) -> Result<Self::ProverMessage, PolyIOPErrors>;
}

/// Trait for sum check protocol verifier side APIs.
pub trait SumCheckVerifier<F: PrimeField> {
    type DomainInfo;
    type ProverMessage;
    type Challenge;
    type Transcript;
    type SubClaim;

    /// initialize the verifier
    fn verifier_init(index_info: &Self::DomainInfo) -> Self;

    /// Run verifier at current round, given prover message
    ///
    /// Normally, this function should perform actual verification. Instead,
    /// `verify_round` only samples and stores randomness and perform
    /// verifications altogether in `check_and_generate_subclaim` at
    /// the last step.
    fn verify_round_and_update_state(
        &mut self,
        prover_msg: &Self::ProverMessage,
        transcript: &mut Self::Transcript,
    ) -> Result<Self::Challenge, PolyIOPErrors>;

    /// verify the sumcheck phase, and generate the subclaim
    ///
    /// If the asserted sum is correct, then the multilinear polynomial
    /// evaluated at `subclaim.point` is `subclaim.expected_evaluation`.
    /// Otherwise, it is highly unlikely that those two will be equal.
    /// Larger field size guarantees smaller soundness error.
    fn check_and_generate_subclaim(
        &self,
        asserted_sum: &F,
    ) -> Result<Self::SubClaim, PolyIOPErrors>;
}

impl<F: PrimeField> SumCheck<F> for PolyIOP<F> {
    type Proof = IOPProof<F>;

    type PolyList = VirtualPolynomial<F>;

    type DomainInfo = DomainInfo<F>;

    type SubClaim = SubClaim<F>;

    type Transcript = IOPTranscript<F>;

    fn extract_sum(proof: &Self::Proof) -> F {
        let start = start_timer!(|| "extract sum");
        let res = proof.proofs[0].evaluations[0] + proof.proofs[0].evaluations[1];
        end_timer!(start);
        res
    }

    /// Initialize the system with a transcript
    ///
    /// This function is optional -- in the case where a SumCheck is
    /// an building block for a more complex protocol, the transcript
    /// may be initialized by this complex protocol, and passed to the
    /// SumCheck prover/verifier.
    fn init_transcript() -> Self::Transcript {
        let start = start_timer!(|| "init transcript");
        let res = IOPTranscript::<F>::new(b"Initializing SumCheck transcript");
        end_timer!(start);
        res
    }

    /// Generate proof of the sum of polynomial over {0,1}^`num_vars`
    ///
    /// The polynomial is represented in the form of a VirtualPolynomial.
    fn prove(
        poly: &Self::PolyList,
        transcript: &mut Self::Transcript,
    ) -> Result<Self::Proof, PolyIOPErrors> {
        let start = start_timer!(|| "sum check prove");

        transcript.append_domain_info(&poly.domain_info)?;

        let mut prover_state = IOPProverState::prover_init(poly)?;
        let mut challenge = None;
        let mut prover_msgs = Vec::with_capacity(poly.domain_info.num_variables);
        for _ in 0..poly.domain_info.num_variables {
            let prover_msg =
                IOPProverState::prove_round_and_update_state(&mut prover_state, &challenge)?;
            transcript.append_prover_message(&prover_msg)?;
            prover_msgs.push(prover_msg);
            challenge = Some(transcript.get_and_append_challenge(b"Internal round")?);
        }

        end_timer!(start);
        Ok(IOPProof {
            proofs: prover_msgs,
        })
    }

    /// verify the claimed sum using the proof
    fn verify(
        claimed_sum: F,
        proof: &Self::Proof,
        domain_info: &Self::DomainInfo,
        transcript: &mut Self::Transcript,
    ) -> Result<Self::SubClaim, PolyIOPErrors> {
        let start = start_timer!(|| "sum check verify");

        transcript.append_domain_info(domain_info)?;
        let mut verifier_state = IOPVerifierState::verifier_init(domain_info);
        for i in 0..domain_info.num_variables {
            let prover_msg = proof.proofs.get(i).expect("proof is incomplete");
            transcript.append_prover_message(prover_msg)?;
            IOPVerifierState::verify_round_and_update_state(
                &mut verifier_state,
                prover_msg,
                transcript,
            )?;
        }

        let res = IOPVerifierState::check_and_generate_subclaim(&verifier_state, &claimed_sum);

        end_timer!(start);
        res
    }
}

#[cfg(test)]
mod test {

    use super::*;
    use ark_bls12_381::Fr;
    use ark_ff::UniformRand;
    use ark_poly::{DenseMultilinearExtension, MultilinearExtension};
    use ark_std::test_rng;
    use std::rc::Rc;

    fn test_sumcheck(
        nv: usize,
        num_multiplicands_range: (usize, usize),
        num_products: usize,
    ) -> Result<(), PolyIOPErrors> {
        let mut rng = test_rng();
        let mut transcript = <PolyIOP<Fr> as SumCheck<Fr>>::init_transcript();

        let (poly, asserted_sum) =
            VirtualPolynomial::rand(nv, num_multiplicands_range, num_products, &mut rng)?;
        let proof = <PolyIOP<Fr> as SumCheck<Fr>>::prove(&poly, &mut transcript)?;
        let poly_info = poly.domain_info.clone();
        let mut transcript = <PolyIOP<Fr> as SumCheck<Fr>>::init_transcript();
        let subclaim = <PolyIOP<Fr> as SumCheck<Fr>>::verify(
            asserted_sum,
            &proof,
            &poly_info,
            &mut transcript,
        )?;
        assert!(
            poly.evaluate(&subclaim.point).unwrap() == subclaim.expected_evaluation,
            "wrong subclaim"
        );
        Ok(())
    }

    fn test_sumcheck_internal(
        nv: usize,
        num_multiplicands_range: (usize, usize),
        num_products: usize,
    ) -> Result<(), PolyIOPErrors> {
        let mut rng = test_rng();
        let (poly, asserted_sum) =
            VirtualPolynomial::<Fr>::rand(nv, num_multiplicands_range, num_products, &mut rng)?;
        let poly_info = poly.domain_info.clone();
        let mut prover_state = IOPProverState::prover_init(&poly)?;
        let mut verifier_state = IOPVerifierState::verifier_init(&poly_info);
        let mut challenge = None;
        let mut transcript = IOPTranscript::new(b"a test transcript");
        transcript
            .append_message(b"testing", b"initializing transcript for testing")
            .unwrap();
        for _ in 0..poly.domain_info.num_variables {
            let prover_message =
                IOPProverState::prove_round_and_update_state(&mut prover_state, &challenge)
                    .unwrap();

            challenge = Some(
                IOPVerifierState::verify_round_and_update_state(
                    &mut verifier_state,
                    &prover_message,
                    &mut transcript,
                )
                .unwrap(),
            );
        }
        let subclaim =
            IOPVerifierState::check_and_generate_subclaim(&verifier_state, &asserted_sum)
                .expect("fail to generate subclaim");
        assert!(
            poly.evaluate(&subclaim.point).unwrap() == subclaim.expected_evaluation,
            "wrong subclaim"
        );
        Ok(())
    }

    #[test]
    fn test_trivial_polynomial() -> Result<(), PolyIOPErrors> {
        let nv = 1;
        let num_multiplicands_range = (4, 13);
        let num_products = 5;

        test_sumcheck(nv, num_multiplicands_range, num_products)?;
        test_sumcheck_internal(nv, num_multiplicands_range, num_products)
    }
    #[test]
    fn test_normal_polynomial() -> Result<(), PolyIOPErrors> {
        let nv = 12;
        let num_multiplicands_range = (4, 9);
        let num_products = 5;

        test_sumcheck(nv, num_multiplicands_range, num_products)?;
        test_sumcheck_internal(nv, num_multiplicands_range, num_products)
    }
    #[test]
    fn zero_polynomial_should_error() {
        let nv = 0;
        let num_multiplicands_range = (4, 13);
        let num_products = 5;

        assert!(test_sumcheck(nv, num_multiplicands_range, num_products).is_err());
        assert!(test_sumcheck_internal(nv, num_multiplicands_range, num_products).is_err());
    }

    #[test]
    fn test_extract_sum() -> Result<(), PolyIOPErrors> {
        let mut rng = test_rng();
        let mut transcript = <PolyIOP<Fr> as SumCheck<Fr>>::init_transcript();
        let (poly, asserted_sum) = VirtualPolynomial::<Fr>::rand(8, (3, 4), 3, &mut rng)?;

        let proof = <PolyIOP<Fr> as SumCheck<Fr>>::prove(&poly, &mut transcript)?;
        assert_eq!(
            <PolyIOP<Fr> as SumCheck<Fr>>::extract_sum(&proof),
            asserted_sum
        );
        Ok(())
    }

    #[test]
    /// Test that the memory usage of shared-reference is linear to number of
    /// unique MLExtensions instead of total number of multiplicands.
    fn test_shared_reference() -> Result<(), PolyIOPErrors> {
        let mut rng = test_rng();
        let ml_extensions: Vec<_> = (0..5)
            .map(|_| Rc::new(DenseMultilinearExtension::<Fr>::rand(8, &mut rng)))
            .collect();
        let mut poly = VirtualPolynomial::new(8);
        poly.add_mle_list(
            vec![
                ml_extensions[2].clone(),
                ml_extensions[3].clone(),
                ml_extensions[0].clone(),
            ],
            Fr::rand(&mut rng),
        )?;
        poly.add_mle_list(
            vec![
                ml_extensions[1].clone(),
                ml_extensions[4].clone(),
                ml_extensions[4].clone(),
            ],
            Fr::rand(&mut rng),
        )?;
        poly.add_mle_list(
            vec![
                ml_extensions[3].clone(),
                ml_extensions[2].clone(),
                ml_extensions[1].clone(),
            ],
            Fr::rand(&mut rng),
        )?;
        poly.add_mle_list(
            vec![ml_extensions[0].clone(), ml_extensions[0].clone()],
            Fr::rand(&mut rng),
        )?;
        poly.add_mle_list(vec![ml_extensions[4].clone()], Fr::rand(&mut rng))?;

        assert_eq!(poly.flattened_ml_extensions.len(), 5);

        // test memory usage for prover
        let prover = IOPProverState::prover_init(&poly).unwrap();
        assert_eq!(prover.poly.flattened_ml_extensions.len(), 5);
        drop(prover);

        let mut transcript = <PolyIOP<Fr> as SumCheck<Fr>>::init_transcript();
        let poly_info = poly.domain_info.clone();
        let proof = <PolyIOP<Fr> as SumCheck<Fr>>::prove(&poly, &mut transcript)?;
        let asserted_sum = <PolyIOP<Fr> as SumCheck<Fr>>::extract_sum(&proof);

        let mut transcript = <PolyIOP<Fr> as SumCheck<Fr>>::init_transcript();
        let subclaim = <PolyIOP<Fr> as SumCheck<Fr>>::verify(
            asserted_sum,
            &proof,
            &poly_info,
            &mut transcript,
        )?;
        assert!(
            poly.evaluate(&subclaim.point)? == subclaim.expected_evaluation,
            "wrong subclaim"
        );
        Ok(())
    }
}